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The purpose of this paper is to examine the empirical relationship between gray directors (non-executive non-independent directors) and executive compensation among companies listed in India’s National Stock Exchange (NSE). The paper also examines the possible interplay of relationships between controlling shareholder duality (controlling shareholder being the CEO), ownership category and executive compensation.

A sample of 438 firms listed in the NSE of India was studied using data spanning five financial years, 2012–2013 to 2016–2017.

Empirical evidence suggests that there is a positive association between the proportion of gray directors on the board and executive compensation. The sensitivity of executive compensation to gray directors is found to be higher among family controlled firms. This research has also found that CEOs who belong to controlling shareholder groups received higher pay than professional CEOs. The authors conjecture that these results suggest cronyism and may contribute to lower levels of corporate governance practices in the country.

The hybrid board structure, which India has adopted with the desire to bring the best of Anglo Saxon and Japanese board philosophies, has paradoxically led to self-serving boards. Exploration of alternative thinking to bring about changes in the regulatory framework is, therefore, necessary.

Serious problems are identified with the philosophy behind board composition mandated by Listing Requirements for Indian firms with empirical evidence showing how the existing rules generate cronyism and unfairness to minority shareholders.

The purpose of this paper is to propose a grey linear control system for regulating the price of China's real estate and provide the necessary support to assist the relevant management departments with their policy making.

A grey state equation of the real estate market price that can reflect both the market supply‐demand price mechanism and the production price mechanism is proposed based on the economic cybernetics. Also, the grey control linear theory is used to demonstrate the disequilibrium fluctuation control system for the China's real estate market with uncertain parameters.

The price disequilibrium fluctuation control system for China's real estate market has been in a critical state. The system would reach a balanced state in 2013, if the real estate price in 2010 and 2011 firstly decreased 244.41 yuan/m2 and 62.33 yuan/m2, respectively, and then increased 60.88 yuan/m2 in 2012. The disequilibrium state will continue for years before it reaches a balanced state.

Due to the complexity of operation of grey numbers, the present technique still cannot analyze the properties of the grey control system exactly and further research is needed.

The modelled results can help the relevant management departments steady China's real estate market by price regulation.

A new approach to study the price regulation system of a real estate market is proposed based on grey linear control theory.

The rise in malaria deaths discloses a decline of global malaria eradication that shows that control measures and fund distribution have missed its right of way. Therefore, the purpose of this paper is to study and evaluate the impact and control of malaria on the independent states of the Sub-Saharan African (SSA) region over the time period of 2010–2017 using Deng’s Grey incidence analysis, absolute degree GIA and second synthetic degree GIA model.

The purposive data sampling is a secondary data from World Developmental Indicators indicating the incidence of new malaria cases (per 1,000 population at risk) for 45 independent states in SSA. GIA models were applied on array sequences into a single relational grade for ranking to be obtained and analyzed to evaluate trend over a predicted period.

Grey relational analysis classifies West Africa as the highly infectious region of malaria incidence having Burkina Faso, Sierra Leone, Ghana, Benin, Liberia and Gambia suffering severely. Also, results indicate Southern Africa to be the least of all affected in the African belt that includes Eswatini, Namibia, Botswana, South Africa and Mozambique. But, predictions revealed that the infection rate is expected to fall in West Africa, whereas the least vulnerable countries will experience a rise in malaria incidence through to the next ten years. Therefore, this study draws the attention of all stakeholders and interest groups to adopt effective policies to fight malaria.

The study is a pioneer to unravel the most vulnerable countries in the SSA region as far as the incidence of new malaria cases is a concern through the use of second synthetic GIA model. The outcome of the study is substantial to direct research funds to control and eliminate malaria.

The purpose of this paper is to develop some grey models to analyze and control the poor information systems, or grey systems.

The grey system theory has been a more widespread application in recent years and the authors have solved many forecast problems of incomplete information with it. However, the establishment of gray control models still needs certain prerequisites.

Based on incomplete information or poor information, by using the viewpoint of the grey system theory and the integral generation operation in this paper, six kinds of grey control models have been established.

The paper offers very useful advice for incomplete (or poor) information control.

The paper is aimed at control engineers and offers a new approach to the optimal choice of information control models.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

The theory and method of the gray model control with removed residuals is used first for the study of active vibration control of a rotor system. For the symmetric rotor bearing system having a single disk, a scheme of gray model control with removed residuals about the rotor vibration is designed in this paper. The results of simulated calculation showed that this control scheme not only has good effectiveness, but also can be realized easily.

The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it commemorates the 40th anniversary of the birth of grey system theory and the 10th anniversary of Grey Systems–Theory and Application.

Firstly, the innovations of theoretical research in grey system theory were summarized and some of the widely recognized new results are briefly described. By searching and combing the research results of grey system theory in China national knowledge infrastructure (CNKI) database and Web of Science by Institute for Scientific Information (ISI), this paper shows the rapid development trend of grey system theory in the past 40 years, and the successful applications of grey system theory in the fields of social sciences, natural sciences and engineering technologies.

More than 227 thousands literature were found by input 10 phrases such as grey system, grey number and sequence operator etc. in CNKI database. After entering the new century, the number of grey system papers included in CNKI database is increasing rapidly. Since 2008, more than 10 thousands papers have been included per year and more than 15 thousands papers have been included per year since 2014. Grey system method and model are widely used in physics, chemistry, biology and other fields of natural science, as well as transportation, electric power, machinery and other fields of engineering technology, and a large number of valuable results have been achieved.

It can be seen that the grey system theory plays an important role in promoting China’s scientific and technological progress, innovation and development and high-level talent training from tens of thousands of literatures marked with important national science and technology projects and a large number of grey system literatures published by China’s double first-class universities and double first-class discipline construction universities.

Both innovations of theoretical research and practical application play important role in the growth of new theory. The innovations of theoretical research provide methods and tools for practical application, which is conducive to improve application efficiency and broaden application fields. A large number of practical applications needs have become the source of theoretical innovation and the solid background for the birth of theoretical innovation achievements.

In this paper, we take a look at the state‐of‐the‐art of the theory and applications of the so‐called grey systems theory founded in the 1980s. After a brief historical review of the development history of this theory, we look at the main blocks of the theory followed by several successful applications. It is our hope that a reader who does not know anything about this branch of scientific exploration will gain a firm understanding of the basics so that the rest of this special issue becomes possible to comprehend.

The purpose of this paper is to present the scientific background from which grey systems theory came into being, the astonishing progress that grey systems theory has made in the world of learning and its wide‐ranging applications in the entire spectrum of science.

The grey uncertainty is compared with other kinds of uncertainty such as stochastic uncertainty, unascertainty, fuzzy and rough uncertainty.

The advances in grey systems theory and its various successful applications are introduced individually by algorithms of grey numbers and grey algebraic systems, grey dynamic models and grey predictions, grey optimization analysis for decision making, grey control models.

Many scientific theories require the unremitting efforts of several generations of people and have gone through hundreds of years before reaching maturity and perfection. Grey systems theory is still in its growth period. So, it is unavoidable that there exist immature and imperfect parts in the theory.

Grey systems theory is a new method for studying problems of uncertainty with few data points and poor information. This new theory studies small samples and systems with poor information, which have partial information known, partial information unknown. It describes adequately and monitors effectively systems' operations and evolutions through extracting valuable information from the little known information. Grey systems theory comes into being along with the development of modern systems science and uncertainty systems theories and methods. It is also a result of deepened perceptivity about uncertain systems.

The purpose of this paper is to introduce the elementary concepts and fundamental principles of grey systems and the main components of grey systems theory. Also to discuss the astonishing progress that grey systems theory has made in the world of learning and its wide‐ranging applications in the entire spectrum of science.

The characteristics of unascertained systems including incomplete information and inaccuracies in data are analysed and four uncertain theories: probability statistics, fuzzy mathematics, grey system and rough set theory are compared. The scientific principle of simplicity and how precise models suffer from inaccuracies are also shown.

The four uncertain theories, probability statistics, fuzzy mathematics, grey system and rough set theory are examined with different research objects, different basic sets, different methods and procedures, different data requirements, different emphasis, different objectives and different characteristics.

The scientific principle of simplicity and how precise models suffer from inaccuracies are shown. So, precise models are not necessarily an effective means to deal with complex matters, especially in the case that the available information is incomplete and the collected data inaccurate.

The elementary concepts and fundamental principles of grey systems and the main components of grey systems theory are introduced briefly. The reader is given a general picture of grey systems theory as a new method for studying problems where partial information is known, partial information is unknown; especially for uncertain systems with few data points and poor information.